Alteration in Sodium Channel Gate Kinetics of the Hodgkin-Huxley Equations Applied to an Electric Field Model for Interaction Between Excitable Cells

An electric field model for electrical transmission of excitation between adjacent myocardial cells, without the necessity of low-resistance connections between the cells, is further developed. The voltage dependency of the membrane conductances was modeled by the Hodgkin-Huxley equations. A major assumption of the model is that the pre-and postjunctional membranes are excitable. The bulk electrical properties (capacitance, conductivity, etc.) of the junctional membranes may be the same as those of the surface membranes. We showed that a modification of the dynamics of the fast sodium channel gates of the junctional membranes (controlled by the m and h parameters) can be employed as a mechanism to secure propagation of an impulse. The propagation velocity was determined primarily by the dynamics of the junctional membranes, and was essentially independent of the rate of rise of the surface units. Propagation at a constant velocity occurred when the electric field model was expanded to a chain of six cells. Thus, the electric field model, based on closely apposed and excitable junctional membranes, could account for propagation in cardiac muscle, and may apply under various physiological and pathophysiological conditions.